An Error-State Model Predictive Control on Connected Matrix Lie Groups for Legged Robot Control

This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra. Moreover, given an initial condition, the linearized tracking error dynamics and equations of motion are globally valid and evolve independently of the system trajectory. By exploiting the symmetry of the problem, the proposed approach shows faster convergence of rotation and position simultaneously than the state-of-the-art geometric variational MPC based on variational-based linearization. Numerical simulation on tracking control of a fully-actuated 3D rigid body dynamics confirms the benefits of the proposed approach compared to the baselines. Furthermore, the proposed MPC is also verified in pose control and locomotion experiments on a quadrupedal robot MIT Mini Cheetah.

Automated summary

This paper presents a new error-state Model Predictive Control (MPC) approach for robot control based on connected matrix Lie groups. By linearizing the tracking error dynamics and equations of motion in the Lie algebra and exploiting the problem's symmetry, the proposed approach achieves faster convergence of rotation and position compared to the current state-of-the-art methods. Numerical simulations and experiments on a quadrupedal robot confirm the advantages of the proposed approach.